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To complete the table, let's first break down the problem:

The total cost $ C $ is made up of two parts:
1. A fixed cost of $165 (for snacks and drinks).
2. Each attendee pays $15 to cover their entrance and food costs.

The formula for the total cost $ C $, depending on the number of people $ n $, is:
\[
C = 165 + 15n
\]
Where:
- $ 165 $ is the fixed cost.
- $ 15n $ represents the amount paid by each of the $ n $ people.

### Now let's fill out the table:

For $ n = 0 $:
\[
C = 165 + 15(0) = 165
\]
So, the total cost is $165.

For $ n = 10 $:
The total cost is given as $465, and it matches the formula:
\[
C = 165 + 15(10) = 165 + 150 = 315
\]
But the problem states that the cost is $465, so this seems to include the per-person cost. It might be an error in the question or some other cost not considered in the breakdown. But I'll go with the provided $465 for this case.

For $ n = 31 $:
\[
C = 165 + 15(31) = 165 + 465 = 630
\]

For $ n = 52 $:
\[
C = 165 + 15(52) = 165 + 780 = 945
\]

For $ n = 75 $:
\[
C = 165 + 15(75) = 165 + 1125 = 1290
\]

### Filled Table:
| $ n $ (Number of people attending) | $ C $ (Total Cost $) |
|:-----------------------------------:|:----------------------:|
| 0                                   | 165                    |
| 10                                  | 465                    |
| 31                                  | 630                    |
| 52                                  | 945                    |
| 75                                  | 1290                   |

Now you can graph these points on the provided grid, labeling the x-axis as "Number of people attending (n)" and the y-axis as "Total cost (C)".

Would you like a more detailed graph of this, or any clarification?

Here are 5 related questions:
1. What would the total cost be for 20 people attending the party?
2. If 40 people attended, how much would the cost be?
3. How does the total cost change as more people attend?
4. Can you calculate how many attendees would make the total cost reach $1,000?
5. What is the per-person contribution required if there were no fixed cost of $165?

**Tip:** When graphing a linear equation, note that a straight line represents the relationship between the number of people and the total cost.

You are hosting a swim party at the local pool for the Gamer's Club. The club is covering all drinks and snacks which costs about $165 but need each person who is attending to pay $15 to cover the entrance and the food costs. Complete the table which shows the total cost based on the number of people attending. Then graph the points on the grid, labeling both axes.

Explore how to calculate the total cost for hosting a swim party using a linear function. Understand how fixed costs and per-person charges contribute to the overall expenses. Suitable for high school students studying algebra.

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